A police officer was punched in the face by a would-be sneaker thief, more concerned with fashion than the law, cops said.

The suspect tried to steal a pair of sneakers from a Brooklyn Heights shoe store before slipping into the Fulton and Hoyt Street train station but he was followed by a police officer, cops said.

The officer tried to arrest the thug who punched him in the face and pushed him down a flight of stairs, making a run for it, law enforcement said.

The officer was taken to a local hospital for injuries to his head, back, and arm, cops said.

Police are looking for the assailant who was wearing a black varsity jacket with red sleeves, a black knit cap, and dark pants. He is described as 6-feet, 190 lbs, with brown eyes and a black beard, police said.